SERVICEABILITY LIMIT STATES OF CONCRETE BEAMS PRESTRESSED BY CFRP BARS
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1 SERVICEABILITY LIMIT STATES OF CONCRETE BEAMS PRESTRESSED BY CFRP BARS by Amr A. Abdelrahman(l) and Sami H. Rizkalla(2) Abstract The non-corrosive and high strength-to-weight ratio characteristics of carbon fibre reinforced plastic, (CFRP), prestressing reinforcements introduce an excellent solution for the deterioration problem of concrete due to corrosion. Due to the significant difference of characteristics of CFRP in comparison to steel, it is extremely important to determine the serviceability limit states of concrete members prestressed by this type of reinforcement. This paper summarizes an experimental program undertaken at the University of Manitoba to study the serviceability of concrete beams prestressed by CFRP reinforcements. The experimental program consisted of testing eight concrete beams prestressed by CFRP bars and two beams prestressed by conventional steel strands. The measured deflection and crack width are compared to the predicted values based on different codes, u~ing the properties of CFRP bars. In addition to the findings of the experimental work, this paper presents theoretical models, proposed to predict deflections prior and after cracking and crack width under service loading conditions. The crack width is predicted using appropriate bond factors of this type of reinforcement. Design guidelines for prestressed concrete beams with CFRP reinforcement are also presented. (1) Ph.D. Candidate. Civil and Geological Engineering Department, University of Manitoba. Winnipeg. Manitoba, Canada. R3T 5V 6. (2) Professor and Program leader of the Canadian Network of Centre of Excellence on Intelligent Sensing for Innovative Structures. FACt FCSCE. FASCE. FEIC.
2 Introduction Use of carbon fibre reinforced plastic, CFRP, as prestressing reinforcement for concrete structures, has increased rapidly for the last ten years. The non-corrosive characteristics, high strength to weight ratio and good fatigue properties of CFRP reinforcement significantly increase the service life of structures. However, the high cost and low ductility of CFRP reinforcement due to its limited strain at failure are problems yet to be solved for the spread use of this new material. Use of partially prestressed concrete members has the advantages of reducing the cost, due to the ability to increase the eccentricity of the prestressing reinforcement, and improving the de formability. However, the deflection and cracking of concrete beams partially prestressed by CFRP reinforcement should be investigated. This study investigates the flexural behaviour of concrete beams prestressed by Leadline CFRP reinforcement, produced by Mitsubishi Kasei, Japan. The various limit state behaviour considered include deflection before and after cracking, crack pattern, spacing and width, strain distribution and failure modes. Several analytical models were adapted to predict the deflection and crack width of the beams. Design recommendations of concrete beams prestressed by CFRP bars are presented. Experimental Program Eight concrete beams prestressed by Leadline CFRP bars were tested, in addition to two concrete beams prestressed by conventional steel strands. The beams were 5.8 meter simply supported span and 330 mm in depth, which represents typical span to depth ratio used for bridge girders. The cross section of the tested beams was T-section with two flange widths, 200 and 600 mm as shown in Figure 1. The two jacking stresses used for the CFRP bars were 50 and 70 % of the ultimate guaranteed strength of the Leadline, reported by the manufacturing company. The level of prestressing and consequently the concrete stress distribution along the section was varied. The distribution of the Leadline bars in the tension zone was also varied to study its effect on the cracking behaviour of the concrete beams prestressed by CFRP bars. A summary of the manufacturing and the testing process of the beams can be found in a separate paper (Abdelrahman and Rizkalla 1995). Flexural Behaviour The two modes of failure, observed in this study, were rupture of the furthest Leadline bar from the neutral axis and crushing of the concrete at the extreme compression fibre within the constant moment zone. At the onset of rupture of the Leadline bar, a horizontal crack occurred, in some of the beams, at the level of the bar as well as extensive cracks extended to the top flange of the beam. The horizontal cracks occurred due to the release of the elastic strain energy after rupture of bars. The released elastic energy, which is partly absorbed by the concrete, resulted in cracking at the level of the bars (Abdelrahman, Tadros and Rizkalla
3 1995). The rupture of the first Leadline bar was followed by a progressive failure of the other Leadline bars. Cracking of the beams, failed by crushing of concrete, was not as extensive as the cracks occurred for the beams failed by rupture of the Leadline bars. No slip of the Leadline bars was observed to any of the two ends of the tested beams. _ beam prestressed by Leadline - beam prestressed by steel 600 OI40----~ ~----~00~---2~00----~----~ Deflection (mm) Figure 1. Load-deflection of beams prestressed by Leadline and steel Typical load-deflection relationship of beams prestressed by Leadline and steel strands, with flange widths of 600 and 200 mm, is shown in Figure l. The four beams had the same jacking force and eccentricity. Beams prestressed by Leadline had similar stiffness to beams prestressed by steel before cracking. After cracking, the stiffness of the beams prestressed by Leadline was less than those prestressed by steel due to the lower elastic modulus of the Leadline. For beams with flange width of 600 mm, the ultimate load was 37 % higher for the beam prestressed by Leadline, however, the deflection at ultimate was 50 % less. For beams with flange width of 200 mm, the ultimate load of the beam prestressed by Leadline was 27 % higher and the deflection at ultimate was the same as the deflection of the beam prestressed by steel, since the failure was controlled by crushing of the concrete. The strain distribution at ultimate for the two types of sections used in this investigation prestressed by Leadline and steel, is shown in Figure 2. The strain distribution marked 1,2 and 3 represents the strain measured at three different locations within the constant moment zone. The strains were measured by demec point stations taking into consideration the initial elastic strain of concrete due to prestressing force.
4 The cracking moment of the tested beams was calculated using two methods based on an assumed rupture strength of the concrete according to the CSA Code A (CPCA Concrete Design Handbook 1995). The flrst method was based on strain compatibility and equilibrium conditions where the continuous increase of the tensile strain in the prestressing bars with the increase of the applied load was included. The second method was based on equation 1 where the cracking moment was calculated in one step. Notation of the equation is given at the end of this paper. Mer - Pee + [/r + ~; ] S b (1) Table 1 shows the measured and the predicted cracking and ultimate loads and mode of failure for all the tested beams. The designation of the beams have the flrst letter either T, R, or S, refers to T-section of 600 mm flange width, rectangular section with flange width of 200 mm and steel reinforcement respectively. The flrst number of the beam designation is either 2 or 4 refers to the number of prestressing rods, while the second number,.5 or.7, refers to the ratio of the jacking to the ultimate guaranteed stress. The last letter in the beam designation, H or V, refers to the configuration of the bars in the tension zone, either horizontal or vertical. Table 1 Comparison between the predicted and the experimental results Beam ~kmd ~d ~kmd Failure P er,exp Per Per Pu,exp P u (len) prdjexp prdjexp (kn) prdj mode methodl meth0d2 methodl method2 exp T-4-.5-H R* R-4-.5-H c t T-4-.5-V R R-4-.5-V R T-4-.7-V R R-4-.7-V R T-2-.5-V R R-2-.5-V R S-T R S-R C Mean 1.22* 1.09*.90 Standard deviation 0.20* 0.17*.03 * Rupture of prestressing reinforcement t Crushing of concrete :j: Mean value and standard deviation for beams prestressed by Leadline Mean value and standard deviation for beams failed by rupture of Leadline bars
5 P = 89.3 len u beam prestressed by Leadline P = 70.1 len u beam prestressed by steel failure due to crushing of concrete (flange width = 200 mm) p = k.n u beam prestressed by Leadline P =77.1 len u beam prestressed by steel failure due to rupture of prestressing reinforcement (flange width = 600 mm) Figure 2. Strain distribution of beams prestressed by Leadline and steel The crack pattern of beams with 600 and 200 mm flange width prestressed by Leadline bars and steel strands is shown in Figure 3. Beams prestressed by Leadline had less number of cracks and consequently larger average spacing between cracks than beams prestressed by steel strands. This behaviour could be attributed to the lower flexural bond strength of the Leadline than steel (Abdelrahman and Rizkalla 1995). Analytical Model Behaviour of beams prestressed by FRP reinforcement was predicted by many researchers using strain compatibility approach (Abdelrahman, Tadros and Rizkalla 1995 and Research Subcommittee on Continuous Fibre Reinforcing Material, JSCE 1993). The results obtained from the analysis were in a good agreement with the experimental results. The Leadline bars are considered in the analysis to be linearly elastic up to failure. The tensile strength of the Leadline, used in the analysis is 2950 MPa, which was evaluated by tension tests performed at the University of Manitoba (Abdelrahman and Rizkalla 1995). It should be mentioned that the guaranteed strength of the Leadline reported by the manufacturing company is 1970 MPa (Mitsubishi Kasei 1992). The elastic modulus of the Leadline used for analysis is 147 GPa. The concrete was represented by a parabolic stress-strain relationship in compression.
6 beam prestressed by Leadline beam prestressed by steel ~ Failure of beams due to crushing of concrete beam prestressed by Leadline Failure of beams due to rupture of prestressing reinforcement Figure 3. Modes of failure of beams prestressed by Leadlinc and steel
7 The cracking load of the beams prestressed by Leadline bars was overestimated using method #1 by an average value of 22 % and a standard deviation of 20 %. Using equation 1, method #2, provided an average ratio between the predicted and the observed cracking load of 1.09 and a standard deviation of 0.17 as shown in Table 1. The cracking load of the two beams with low reinforcement ratio, beams prestressed by two Leadline bars, were overestimated by about 55 % using the flrst method and 35 % using the second method. This may be attributed to the variability of the rupture strength. It could be also attributed to the increased shrinkage cracks in the beams with two Leadline bars in comparison to the beams prestressed by four bars. The predicted cracking load of the two beams prestressed by steel was overestimated by 7 %, using strain compatibility and equilibrium conditions, and underestimated by 5 % using the second method, as shown in Table 1. The predicted failure loads of beams prestressed by Leadline and failed by rupture of the Leadline bars were underestimated by an average value of 10 %, as shown in column 9, Table 1. This may be attributed to the higher tensile strength of the Leadline bars than the assumed value which is 2950 MPa. The predicted failure load of the beam prestressed by Leadline and failed by crushing of concrete was the same as the observed failure load, as shown in Table 1. The predicted failure load of the beams prestressed by steel was 7 % less than the observed value for the beam failed by rupture of the steel strands and it was the same as the measured value for the beam failed by crushing of concrete. The predicted failure mode of the tested beams prestressed by Leadline and steel agreed with the observed failure mode. Accordingly, one beam prestressed by Leadline, R-4-.5-H, failed by crushing of concrete. All the other beams prestressed by Leadline failed by rupture of the Leadline bars. Also, the beam prestressed by steel strands with 200 mm flange width failed by crushing of concrete, while the beam with 600 mm flange width failed by rupture of the steel strands. Deflection Prediction Four methods were used to predict the deflection, taking into consideration the tension stiffening. The deflection was calculated based on integration of the mean curvature along the span of the beam for the flrst three methods. The four methods are described as follows: 1- The effective moment of inertia Ie method modifled by Tadros, Ghali and Meyer (1985) was used to predict the deflection of the tested beams. It is reported that this method gives the most accurate prediction of the deflection compared to the different methods using Ie approach (Krishna Mohan Rao and Dilger 1992). Equations 2 to 4 were used to predict the effective moment of inertia and the effective centroidal distance, which were used to evaluate the effective curvature <1>e using equation 5. Notation of the equations is given at the end of this paper.
8 (2) 11,4 Ye - Ycr + 'f' (3) (4) (5) 2- The CEB-FIP Code (CEB-FIP Code 1990) was used to calculate the mean curvature <Pm using the interpolation factor ~ between the curvature of the gross section and the cracked section, <Pg and <Per' respectively, as given by equations 6 and 7. The factor ~l' refers to the bond condition of the reinforcement and the factor ~2 refers to the type of the applied load. As the beams were tested under static short-term loading, the coefficient ~2 was taken equal to 1.0, as recommended by the code. The factor ~1 was evaluated for the beams prestressed by Leadline and found to be equal to 1.0 in comparison to a value ranging from 0.4 to 0.8 for steel bars. <Pm - (l-~)<pg+~<pcr (6) J ~ ~ 1 ~ 2 M cr - M de ( Ms - Mde ~ 0.4 (7) 3- The mean curvature was calculated based on strain compatibility including the tensile strength of the concrete. The proposed stress distribution within the cross section is shown in Figure 4. The tensile stresses in concrete were introduced in two locations on the tension side of the beam, below the neutral axis where the tensile stresses in concrete increases linearly up to the rupture strength and secondly on the effective embedment zone around reinforcement. The average tensile stress of concrete after cracking is given by equation 8 (Collins and Mitchell 1991). The calculated value of the factor 0. 1, which represents the bond condition of the reinforcement, was 0.6 for beams prestressed by Leadline, in comparison to a value of 0.7 for steel strands.
9 Ict J 500 e ct e ct > e r (8) r --, ~--,n-- _~.A: L Q.. ~b-+ effective T w cross section strain diagram actual concrete stress equivalent stresses internal forces +I-----b-----+I e Figure 4. Strain compatibility of prestressed concrete section accounting for concrete in tension 4- A simplified method was used to calculate the deflection using Ie approach. The deflection was calculated using equation 9, based on Ie given by equation 10. After cracking and due to tension stiffening, the distance of the centroidal axis of the section from the extreme compression fibre Y e has an intermediate value between the cracked and uncracked centroidal distances Ycr and Yg respectively. Equation 11 is proposed to calculate the effective centroidal distance Ye' which is used in equation 9. (9). (10) Ye - Y cr + ~ (Y g - Y cr ) (11)
10 Prediction of the deflection, within 20 % error from the measured values, for the first three described methods were 85, 94 and 92 %, respectively while it was 73 % using the simplified method. This analysis suggests that the calculation of the deflection based on integration of the curvature along the span using any of the three methods gives an excellent correlation with the measured deflection. The simplified method is also shown to be a good tool for preliminary design. It should be noted that bond factors should be evaluated when using either the CEB-FIP Code or the analysis based on strain compatibility, while equivalent moment of inertia, Ie' method is applicable to any type of reinforcement. Figure 5 shows the predicted deflection for a typical beam prestressed by Leadline using method 3 and ~ ~ 100 beam R-4-.5-H z ~ 80 '-' 60 ~ c:: o...j experimental strain cmpatibility accounting for concrete in tension simplified method O ~------~~========~======~ Deflection (mm) Crack Width Prediction Figure 5. Predicted deflection using method 3 and 4 The crack width was calculated for all the tested beams prestressed by CFRP bars using three methods given by Suri and Dilger (1986), CEB-FIP Code (1978) and Gergely and Lutz (1966). Since bond characteristics of the reinforcement considered to be one of the most important parameters affecting the cracking behaviour of partially prestressed beams, the three methods were used to determine the equivalent bond factors for CFRP bars. The bond factors were found to be different from steel reinforcements since it is significantly affected by the surface conditions (smooth or ribbed) and type of reinforcement (strand or bar). The other two factors which could
11 also affect the bond characteristics are the elastic modulus and poissoin's ratio (Abdelrahman and Rizkalla 1995). The following subsections discuss each of the above methods. 1- The proposed method by Suri and Dilger (1986) given by equation 12 was adapted by the CPCI Design Manual (1989) to estimate the maximum crack width at the beam soffit. The bond factor k was calculated using linear regression analysis of the test results, and a value of 1.41 x 10-6 was obtained for Leadline in comparison to values ranging from 2.55 x 10-6 to 4.50 x 10-6 for the different combinations of prestressed and non-prestressed steel. The calculated and the measured crack widths, using this method, were within 40 % accuracy. (12) 2- The CEB-FIP Code (1978) expression for calculating the crack width using the average spacing between cracks is given by equations 13 and 14. The factor t;; shown in equation 14 is given by equation 7. The average crack width, w m ' at the beam soffit is estimated using the strain of the prestressing reinforcement after decompression and the crack spacing. To evaluate the bond factor Itkl It in equation 13, two values, 0.2 and 0.8, were selected as initial values for the bond factor. The error of the calculated crack width was interpolated and a value of 0.28 was estimated for the bond factor. The average crack width of the tested beams was predicted and found to be ± 40 % of the measured crack width. s S rm - 2 ( c + 10 ) + ki k2 - Pr (13) d p (14) 3- Gergely and Lutz (1966) recommended the use of equation 15 for the calculation of the maximum crack width at the beam soffit, for reinforced concrete beams. The same equation is proposed for concrete beams partially prestressed by steel reinforcement by the CPCI Design Manual (1989). The bond factor R was modified by Suri and Dilger (1986) and it was found to be ranging from 13.7xlO- 6 to 25xlO- 6 for beams prestressed by steel. The factor R, which was linearly interpolated, has a value of 12.5xlO- 6 for beams prestressed by Leadline. The predicted crack width for the tested beams, using equation 15 is compared to the measured values and an acceptable agreement within ± 40 % was obtained. w - R h2,--- is 3y de A hi (15)
12 The difference between the measured and the predicted crack width was within 40 % for the three methods. The least standard deviation of this difference was 15 % for Gergely and Lutz method. Therefore, it is essential to verify the proposed values for the bond factors for other beams with wide range of span-todepth ratio and different configurations. Conclusions Eight concrete beams prestressed by Leadline CFRP bars were tested to investigate the flexural behaviour of such beams. Analytical models were used to predict the deflection and the crack width of the beams. The following conclusions can be drawn from the study: 1- Deflection of beams prestressed by Leadline is equivalent to the deflection of beams prestressed by steel provided that the failure is controlled by crushing of the concrete in the compression zone. If the failure is governed by rupture of the Leadline bars, the deflection -at failure is considerably small in comparison to equivalent beams prestressed by conventional steel strands. 2- Beams prestressed by Leadline had less number of cracks and higher average crack spacing than beams prestressed by steel strands. This could be attributed to the lower flexural bond of the Leadline. 3- Accurate prediction of the deflection of beams prestressed by Leadline should account for the tension stiffening of concrete. Based on 20 % difference, the integration of curvature method along the beam span has an accuracy of about 90 %, while the simplified method has an accuracy of 73 % which is sufficient for preliminary design purpose. 4- Crack width can be predicted within 40 % accuracy using equivalent bond factors proposed in this study. Notation A = Acef = Ag = ~ : b = c = db = de = d ps = e = average effective area around one reinforcing bar effective area of concrete (CEB-FIP 1978) gross cross sectional area area of prestressing reinforcement total area of prestressed and non-prestressed reinforcement breadth of the beam concrete cover measured from surface of reinforcement bar diameter concrete cover measured from centre of reinforcement depth of prestressing reinforcement eccentricity of the prestressing reinforcement based on gross section
13 Ee = f et = ~ = hi = h2 = k = kl = k2 = = 1), = ks = Mer = Mde = Ms = Mu = L = P e = s = So = Srrn = Wmax Yer = Ye = Yg = ~ = d = E et = Es2 = <1> er = <1>g = <1>e = Pr = = properties elastic modulus of the concrete tensile strength of the concrete rupture strength of the concrete distance from centroid of tensile reinforcement to neutral axis distance from extreme tensile fibre to neutral axis bond factor coefficient, depends on bond of reinforcement coefficient, depends on the shape of the strain diagram 0.25 [(E 1 + E 2 ) I 2E 1 ], where El and 2 are strain values in the cracked state at the top and bottom of the zone considered, respectively. factor for the calculation of the deflection due to the prestressing reinforcement, depends on the shape of the strand factor for the calculation of the deflection due to the applied loads depends on the shape of the loading and boundary conditions cracking moment decompression moment service moment ultimate moment span of the beam effective prestressing force spacing between longitudinal reinforcement section modulus of the tension side. average spacing between cracks maximum crack width at the beam soffit distance between the centre of gravity of the section and the compression fibre based on cracked section properties distance between the centre of gravity of the section and the compression fibre accounting for tension stiffening distance between the centre of gravity of the section and the compression fibre based on gross section properties ~1 ~2' where ~I is a bond factor, which is calculated for Leadline based on the measured deflection and found to be equal to 1.0, and ~2 is a factor depends on type of loading deflection of the beam tensile strain of the concrete strain in the prestressing reinforcement after decompression curvature of the section based on cracked section analysis curvature of the section based on gross section analysis curvature of the section accounting for tension stiffening As I Acef
14 References 1- Abdelrahman A.A. and Rizkalla S.H., (1995) "Serviceability of Concrete Beams Prestressed by Carbon Fibre Reinforced Plastic Rods", Proceeding of the Second International RILEM Symposium (FRPRCS-2), Non Metallic (FRP) Reinforcement for Concrete Structures, Ghent, Belgium, August, pp Abdelrahman A.A., Tadros G., Rizkalla S.H., (1995) "Test Model for the First Canadian Smart Highway Bridge", ACI Structural Journal, Vol.92, No.4, July August, pp Canadian Prestressed Concrete Institute CPCI (1989) "Metric Design Manual, Precast and Prestressed Concrete", Ottawa, Canada, Second Edition, Second Printing, 340p. 4- Collins, M. and Mitchell, D. (1991) "Prestressed Concrete Structures", Prentice Hall, Englewood Cliffs, New Jersey, 766p. 5- Comit~ Euro-International Du B~ton (1978) "CEB-FIP Model Code for Concrete Structures.", 3rd Edition, 348pp. 6- Comit~ Euro-International Du Beton (1993) "CEB-FIP Model Code 1990", Design Code, Thomas Telford, Great Britain, 416p. 7- Concrete Portland Cement Association CPCA (1995) "Concrete Design Handbook" Second Edition, Ottawa, Ontario, August, 485p. 8- Gergely, P., and Lutz, L. (1966) "Maximum Crack Width in Reinforced Concrete Flexural Members", Causes, Mechanism, and Control of Cracking in Concrete, ACI Publication SP-20, pp Krishna Mohan Rao, S.V. and Dilger, W.H. (1992) "Evaluation of Short-Term Deflections of Partially Prestressed Concrete Members", ACI Structural Journal, V.89, No.1, January-February, pp Mitsubishi Kasei Corporation, (1992) "Leadline Carbon Fibre Tendons/Bars", Product Manual, December, 75p. 11- Research Subcommittee on Continuous Fibre Reinforcing Material (1993) "English translation of the report of the JSCE", Japan Society of Civil Engineering, Japan, l20p. 12- Suri, K.M., and Dilger, W.H. (1986) "Crack Width of Partially Concrete Members", ACI Journal, Vol. 83, No.5, September-October, pp Tadros, M., Ghali, A. and Meyer, A. (1985) "Prestress Loss and Deflection of Precast Concrete Members", PCI Journal, Vo1.30, No.1, January-February, pp.1l4-141.
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